Three Dimensional Sudoku Cube Puzzle

ABSTRACT

A three-dimensional Sudoku game comprising a plurality of individual Sudoku puzzles arranged on the faces of a polyhedron, in which cells on the edges of each face of the polyhedron must contain the same number or other symbol as adjacent cells on adjoining faces of the game, such that a plurality of Sudoku puzzles must be solved together.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of priority from U.S. Provisional Patent Application No. 61/232,419, filed Aug. 8, 2009 and entitled THREE DIMENSIONAL SUDOKU CUBE PUZZLE, the entire disclosure of which is hereby incorporated by reference in its entirety.

BACKGROUND

Sudoku (sometimes spelled Su Doku) puzzles are numerical logic puzzles that use a nine-by-nine grid of squares. The squares are grouped into nine regions, each containing nine squares in a three-by-three grid. The puzzle, which is predetermined by the game creator, includes numbers in some of the squares, with the goal of the game being to fill in the empty squares so that the numbers 1 through 9 appear just once in every row, column, and region of the puzzle.

The puzzle's origin dates back to the 18th century, when Swiss mathematician Leonhard Euler invented a puzzle called Latin Squares. The modern day Sudoku puzzle originated in 1979 when a grid titled “Number Place” was published in an American puzzle magazine. By the early 1980's, the puzzle was renamed Sudoku (which means “single number”) and appeared in several Japanese magazines. In 2004, the first Sudoku puzzle was published in a London newspaper.

Sudoku puzzles were originally available only in printed form, appearing in newspapers, magazines, and books. Recently, however, Sudoku board games and computer games played on desktop computers, cell phones and arcade style devices have begun to appear on the market.

United States Patent Publication No. 20070267813 discloses a three dimensional Sudoku game which is played in a manner akin to a Rubik's cube, by having a player solve the cube by manipulating conjoined cubiform elements having numbers on each side. Another type of three-dimensional Sudoku puzzle, made up of nine Sudoku puzzles layered on top of each, other was also published in the Weekend supplement of The Daily Telegraph on May 21, 2005 as the “Dion Cube puzzle.” In this game, each plane through the cube formed a valid puzzle.

SUMMARY

The present invention is a three dimensional, Sudoku-like game having faces which are joined to form a three-dimensional shape, such as a cube, in which the solutions to individual Sudoku puzzles played on each face are constrained by the numbers or other symbols occupying cells in an adjoining face of the game. All of the individual Sudoku puzzles of the present game must therefore be played together as a larger, single puzzle.

In one embodiment, the present game is a three-dimensional game having at least 6 faces, wherein each face comprises 4 sides, each of the 4 sides comprising an edge shared with a different face, wherein:

-   -   each face comprises a plurality of cells arranged in parallel         rows and parallel columns, wherein the rows and columns are not         parallel;     -   each row and each column of a face comprises N² cells, thereby         forming an array of N²×N² cells on each face, wherein N is a         whole number greater than 1, and;     -   each face comprises N² regions, each region comprising N rows of         N cells each and N columns of N cells each;     -   each cell comprises 4 edges that form a parallelogram;     -   each edge of a cell is shared with a different cell, wherein         cells that share an edge can be arranged either on the same face         or can each be on a different, adjacent face; and     -   each cell can comprise one symbol in a non-repeating series of         symbols, wherein each symbol in the series of symbols appears         only once in each row, column, and region of a face,     -   wherein when a first cell on a first face shares an edge with a         second cell on a second face, the first cell and the second cell         must comprise the same symbol.

In the foregoing embodiment, the symbols are preferably numbers, and N is preferably 2, 3, or 4.

A three-dimensional Sudoku game according to the present invention can also comprise:

a plurality of faces, each face comprising a plurality of sides, wherein each of the sides comprises an edge shared with a different face;

a plurality of cells on each face, wherein the cells of each face are arranged in rows and columns, each row and each column of the face comprising N cells, wherein N is a whole number greater than 1, thereby forming an array of N² cells on each face of the game; and

N regions on each face, each region comprising N rows of N cells each and N columns of N cells each,

wherein each cell includes no more than one symbol in a non-repeating series of symbols, each symbol in the series of symbols appearing only once in each row, each column, and each region of a face, and a first cell of a first face of the game and a second cell of a second face must include the same symbol if the first cell and second cell are adjacent.

The symbols are preferably an ordered series of numbers, and N preferably is selected from the group consisting of 4 and 9 in this embodiment. Each cell is also preferably in the form of a square, and each row of a face is arranged perpendicularly to each column of the face. The faces in this embodiment can each be in the form of a square and be arranged to form a cube. The present game is preferably in three-dimensional physical form, but can also be displayed in two dimensions, such as on a computer screen or piece of paper. If the game is in physical form, it can be formed from a rigid planar material such as paper or cardboard which is folded into a three-dimensional object, with each face of the object comprising a face of the game.

The present invention can further comprise a method of playing a three-dimensional Sudoku game, comprising the steps of:

providing a plurality of faces which form at least part of a polyhedron, each face comprising a plurality of sides and N regions, each region comprising N rows of N cells each and N columns of N cells each, wherein N is a whole number greater than 1;

assigning a different symbol from a group of N² non-repeating symbols to each cell in each row of each face;

assigning a different symbol from the group of N² non-repeating symbols to each cell in each column of each face; and

assigning a different symbol from the group of N² non-repeating symbols to each cell in each region of the face,

wherein at least a first face and a second face of the polyhedron are joined at an edge, and adjacent cells on the first face and the second face are assigned the same symbol from the group of N² non-repeating symbols.

A further embodiment of the present invention can comprise a method of generating a three-dimensional Sudoku game in which each cell of the game can comprise a symbol from a predetermined set of symbols, wherein each symbol of the set appears only once in each row, column, and region of a face of the game, comprising:

(a) generating a plurality of faces, each face comprising N² cells, the cells are arranged into rows of N cells and columns of N cells;

(b) assigning a top edge, a bottom edge, a right edge, and a left edge to each cell;

(c) mapping each cell such that the top edge of a cell is the bottom edge of an adjacent cell in a column and such that a right edge of the cell is the left edge of an adjacent cell in the row;

(d) randomly selecting a previously unselected cell of a face of the game and randomly assigning a symbol to the cell from the predetermined set of symbols, thereby generating a randomly assigned cell containing the symbol, the symbol must be different from other symbols contained in other cells in the same row, column and region as the randomly assigned cell, and when the randomly assigned cell shares an edge with a second cell on a different face of the game, the randomly assigned cell and the second cell must comprise the same symbol;

(e) selecting a remaining cell in the game and determining whether the remaining cell can comprise only one valid choice of symbols, and if so, assigning the valid symbol to the remaining cell to generate a nonrandomly assigned cell, and removing the valid symbol from the set of predetermined symbols assignable to other cells in the same row, column and region of the nonrandomly assigned cell; and

(f) repeating steps (d) and (e) until a symbol from the predetermined set of symbols has been assigned to each cell of the game, thereby generating a solved game.

DRAWINGS

FIG. 1 is a perspective view of a cube embodying the present game in the finished state showing three faces of the game, with each face comprising nine rows and nine columns of cells.

FIG. 2 is a plan view of the cube shown in FIG. 1 in a flattened depiction which shows all six faces of the cube in one view.

FIG. 3 is a plan view of an embodiment of the present game showing a face comprising nine rows and nine columns of cells, as in the embodiment of FIG. 1.

FIG. 4 is a perspective view of a cube embodying the present game in the finished state showing three faces of the game, with each face comprising four rows and four columns of cells.

FIG. 5 is a plan view of the cube shown in FIG. 4 in a flattened depiction which shows all six faces of the cube in one view.

FIG. 6 is a plan view of an embodiment of the present game showing a face comprising four rows and four columns of cells, as in the embodiment of FIG. 4.

FIG. 7 is a plan view of two adjacent cells of the present game.

FIG. 8 is a perspective view of a folded embodiment of the present game.

FIG. 9 is a flow chart describing a process for generating the present game.

DESCRIPTION Definitions

As used herein, the following terms and variations thereof have the meanings given below, unless a different meaning is clearly intended by the context in which such term is used.

“Adjacent,” with respect to cells of the present game, refers to a logical association between two cells which is usually depicted by a physical and/or visual association between the two cells, such as a shared boundary.

“Cell” refers to a physical or visually displayed area on a face of the present game for retaining and displaying a number or other symbol.

“Column” refers to an ordered series of cells on a single face of the present game which intersects with other ordered series of cells on the same face designated as rows. The columns on a face are non-intersecting. Typically, rows and columns are laid out on a grid comprising parallel rows and parallel columns, with the rows being perpendicular to the columns.

“Computer-readable medium” refers to an electronic, magnetic, optical, or other physical device or structure that can contain and/or store a computer program. Examples of such media include magnetic computer disks, optical disks, random access memory (RAM), read-only memory (ROM), and erasable programmable read-only memory (EPROM or Flash memory).

“Corner” refers to a logical association between three cells of the present game, and is generally depicted physically and/or visually as the point at which three or more faces of the present game meet.

“Edge” refers to a side formed at the joining and/or intersection of two faces of the present game.

“Face” refers to a group of cells associated with each other in rows, columns, and regions according to Sudoku rules. A face of the present game is generally a physical or visually depicted surface of a cube, and comprises a Sudoku puzzle.

“Polyhedron” refers to a three-dimensional shape whose faces are polygons.

“Random” in the context of the present method of generating a three dimensional Sudoku game means having no specific pattern, arrangement and/or predictable outcome. It is to be understood that the selection of a first cell of a game to which a symbol or value is to be assigned in the present method may be predetermined in a particular embodiment of the game, i.e. the same cell of a face may be consistently selected when generating puzzles, and/or the same symbol may be assigned in this first selection step, without departing from the randomness of this step, as the puzzle comprises no pattern or arrangement prior to such selection step.

“Region” refers to a square block of cells on a face of the present game having N² cells, where N is at least 2, and is typically 2 or 3. In a nine-by-nine Sudoku cube game there are nine regions on each face of the game having nine cells each, while in a four-by-four game there are four regions on each face having four cells each.

“Row” refers to an ordered series of cells on a single face of the present game which intersects with another ordered series of cells on the same face designated as a column. The rows on a face are non-intersecting.

“Side” refers to a peripheral portion (outer boundary) of a cell or a face of the present game, as the case may be. The side of a face of the present game is comprised of the sides of adjacent cells. The side of a cell or face is joined at each end to another peripheral portion of the cell or face, and such sides are preferably depicted as being straight, though this is not required.

“Sudoku puzzle” or “Sudoku game” refers to a puzzle in which N⁴ non-repeating symbols (usually numbers, with N typically being 2 or 3) must be placed into an associated group of cells so that each row, column, and region in which the cells are arranged contains only one of the symbols. The symbols used are typically an ordered series of numbers, e.g. the numbers 1-4 for a puzzle having four rows and four columns on each face. As used herein, such symbols are sometimes referred to as having a “value” without limiting the type of symbol being referred to.

As used herein, the term “comprise” and variations of the term, such as “comprising” and “comprises,” are not intended to exclude other additives, components, integers or steps. The terms “a,” “an,” and “the” and similar referents used herein are to be construed to cover both the singular and the plural unless their usage in context indicates otherwise.

Rules

In the present game, each face of the game comprises a puzzle solvable using the rules of Sudoku games, typically using traditional Sudoku rules. As in traditional Sudoku, a face of the present game comprises N regions with each region having N rows of N cells each and N columns of N cells each, with N being a number greater than 1. Typically, N is 4 or 9, though other values are possible, and the square root of N is typically a whole number. Game play using this configuration of cells under traditional Sudoku rules is as follows:

1. A single, different symbol from a group of N non-repeating symbols (usually an ordered series of numbers) must be assigned to each cell in each row of the face;

2. A different symbol from the same group of N non-repeating symbols must be assigned to each cell in each column of the face; and

3. A different symbol from a group of N non-repeating symbols must be assigned to each cell in each region of the face.

In view of these rules, duplicate symbols are not permitted in any column, any row, or any region of a face. Each face will comprise one or more symbols which are pre-assigned to cells on that face (following the rules above) prior to the start of game play by a user, and typically each region will comprise one or more symbols which are pre-assigned to cells of that region of the face.

In addition to the foregoing rules, additional rules apply to adjacent cells 40 on different faces of the present game 1. In particular, cells 40 on different faces 10 of the present game 1 which are adjacent to each other must be the same. The present game 1 comprises a plurality of faces 10 which are arranged such that each side of a face 10 borders a side of another face of the game at an edge 4. Each cell on a first face which has a side on that edge is adjacent to a cell on the second face which has a side on that edge, and such adjacent cells on the first and second face (i.e., on faces whose sides share a common border or edge 4) must hold the same symbol. An example of this rule is demonstrated for example in FIG. 1, where the bottom side 24 of the top face 13 shares a common edge 4 with the top side 23 of the front face 11. As shown in this figure, the row 32 of cells 40 on the bottom side 24 of the top face 13 contains the numbers “854192376,” and the row of cells on the top side 23 of the front face 11 likewise contains the numbers “854192376,” with adjacent cells on the front face 11 and the top face 13 containing the same number.

A corollary of this rule is that when more than two cells 40 are adjacent to each other, the same symbol must be assigned to all such adjacent cells. This occurs at corners, such as the corner 6 formed in FIG. 1 where cells 40 of the top face 13, the front face 11, and the right face 15 contact each other (in FIG. 1 these cells are illustrated as including the number 6; in FIG. 4 the cells at this corner all include the number 1).

In alternative embodiments, the present game can employ rules used in variants of a traditional Sudoku game. For example, in the variant known as “Greater Than Sudoku,” cells are filled with an ordered series of symbols (usually numbers), and a relationship between the symbols in adjacent cells is specified with respect to which of the symbols can be greater than the other (i.e., appearing later in the ordered series of symbols). The relationship between such adjacent cells is usually specified graphically with symbols such as “>” or “<.” Traditional Sudoku rules as well as the additional rules for the present game specified above also apply when such variant games are played.

Game Elements

The present game 1 can exist in a variety of forms, e.g. in physical or virtual form, and can also comprise a variety of shapes. The game is played on the surfaces (faces) of a polyhedron, such as a cube. Preferably, all surfaces of the game can be viewed by a player of the present game, either by physical manipulation of a game embodied in a physical object or by manipulation of a virtual object displayed on a screen. However, in some embodiments only a subset of the faces of a polyhedron on which the present game is played are viewed by a player.

FIG. 1 is a perspective view of an embodiment of the present Sudoku game 1 in the shape of a cube. Each face 10 of the present game 1 comprises a grid of cells 40 laid out in rows 32 and columns 34 (illustrated in FIGS. 3 and 6), preferably in a planar fashion. In a nine-by-nine cube there are nine rows and nine columns on each face, while in a four-by-four game there are four rows of four cells and four columns with four cells on each face.

The cells 40 of the present game 1 retain symbols, such as numbers, which can be in physical or virtual form. In physical embodiments of the present game the cells 40 comprise a physical space, while in electronically enabled embodiments cells will generally comprise a visually displayed area (such as an area displayed on a monitor or touch screen). Cells generally have four contiguous sides and are typically square in configuration, as shown e.g. in FIG. 7, but they can also comprise other configurations, such as in the “greater than” variant of Sudoku.

The side 41 of a cell 40 of the present game 1 is used as a referent, to indicate an association between the cell and another cell of the game. A side 41 of one cell 40 which is associated with another side of a second cell is described herein as being adjacent to the second cell. In the illustrated embodiments, this association is usually depicted by a shared boundary between a first cell and second cell. For example, in the embodiment shown in FIG. 4, the top row 35 of the right face 15 comprises the numbers 1-2-3-4, and in this row the cell holding the number “2” shares a boundary with the cells displaying “1” and “3” in the same row 35.

In the present game, cells 40 typically have four sides 41, and for ease of depiction are illustrated as a four-sided planar shape, generally a square. The four sides 41 of a cell 40 in such embodiments are termed herein the top side 43, bottom side 44 (positioned opposite the top side 43), right side 45, and left side 46 (positioned opposite the right side 45), as illustrated in FIG. 7. It is to be understood that such designations are for convenience and are used in order to refer to associations between cells rather than to necessarily define a particular spatial orientation of such cells. Using this terminology, the top side 43 of one cell 40 is associated with the bottom side 44 of an adjacent cell, and the right side 45 of a cell is associated with the left side 46 of an adjacent cell. Such adjacent cells are generally physically and/or visually depicted as sharing a common boundary line, particularly in the illustrated embodiments in which cells are arranged in a grid. However, for purposes of depicting and/or playing the present game, the cell sides need not be in contact with one another and can be depicted differently, as in FIG. 7, as long as such sides are associated with each other according to the present game rules. In embodiments in which cells share a common boundary, as shown in the embodiments of FIGS. 1 and 4, the line forming the right side 45 of a particular cell can be the same line which forms the left side 46 of an adjacent cell.

Each face 10 of the present game 1 is in the form a polygon whose outer periphery is composed of a finite sequence of line segments, i.e. sides 20. Faces 10 of the present game 1 are typically planar and in the form of a square or other parallelogram.

FIG. 1 shows a completed game of the present invention having nine rows and nine columns, with all numbers filled in and following the rules of the present game. FIG. 2 illustrates the same game shown in FIG. 1, but with the six faces “unwrapped” from the cube and flattened out to illustrate a complete game. The present game 1 can be played in this form, though most players will likely prefer a three-dimensional representation such as that of FIG. 1. As can be seen from these figures, a cell 40 on an edge 4 of one face must comprise the same symbol as the adjacent cell of a second face. For example, the cells on the right side 25 of the front face 11 must be identical to their adjacent cells on the left side 26 of the right face 15. A valid placing of a number in any one of the cells on an edge must, either automatically or by following the rules, result in the same number being placed in the adjacent cell. In game play, each cell 40 on an edge affects both the row 32, column 34 and region 36 of the face on which it is located as well as the row 32, column 34 and region 36 in which the cell adjacent to it on the other face is located, so both faces must be considered when placing a number in an edge cell.

FIGS. 1 and 2 also illustrate that cells that are adjacent to each other in the corners of a cube must share the same symbols (numbers). As shown in FIG. 1, the top right corner of the front face 11, the top left corner of the right face 15, and the bottom right corner of the top face 13 must all be the same number (“6” in FIG. 1). Whether the game is played in paper form, electronic form, or otherwise, a valid placing of a number in any one of those three cells must, either automatically or by following the rules, place the same number in the other two cells. In game play, a corner cell affects the row 32, column 34 and region 36 of which it is a part as well as a row 32, column 34 and region 36 of the two other faces 10 adjacent to it, so all three faces must be taken into account when placing a number in a corner cell.

FIG. 3 depicts a face 10 of a nine-by-nine game such as that shown in FIGS. 1 and 2, with the numbering however indicating the ordering of rows 32 and columns 34 on the face 10. The face 10 includes nine regions 36, each comprising three rows of three cells each and three columns of three squares each, arranged to form a square. Each of the cells of one of the regions in this figure includes the letter “a” for illustrative purposes.

FIGS. 4 and 5 illustrates a completed game of the present invention having six faces 10 arranged as a cube, each face 10 having four rows 32 and four columns 34, with all numbers filled in and following the rules of the present game. FIG. 6 shows a face 10 of a four-by-four puzzle game such as that illustrated in FIGS. 5 and 6, with the numbering however indicating the ordering of rows 32 and columns 34 on the face 10. The face 10 in this embodiment includes four regions 36, each comprising two rows of two cells each and two columns of two squares each, arranged to form a square. Each of the cells of one region in this figure includes the letter “a” for illustrative purposes.

Game Forms

The present game 1 can be embodied in a number of different forms, but most commonly will comprise either a three dimensional physical object or an image of such an object generated by a computer program. In one embodiment, the faces of the game are formed from a substrate, such as paper, cardboard, or plastic, which is sufficiently rigid to be able to form a polyhedron on which the present game can be played. In this embodiment, the cells and pre-assigned numbers or other symbols of the game are preferably printed onto the substrate. The substrate can for example be planar and can be initially formed as a blank, after which it is folded into a cube or other shape for game play. Alternatively, the game can be formed from a material that is molded into a desired polyhedral shape.

An embodiment of the present game 1 in physical form is illustrated in FIG. 8, which shows an embodiment of the present game formed from a sheet of cardboard. In this embodiment, a cardboard blank comprises the faces 10 of the present game 1 with indicia printed thereon as well as hingedly connected flaps 16 which assist in forming and maintaining the physical structure of the game 1 once the flaps 16 are folded or bent and the game 1 is assembled. The arrows in FIG. 8 indicate the folding of flaps 16 and faces 10 in order to form a game 1. Adhesives can also be used to associate or secure faces 10 to each other in this embodiment.

Alternatively, the present game 1 can be implemented in electronic form by a computer or other electronic device capable of generating a visual display comprising the present game 1. In this embodiment, the game can be embodied in instructions contained in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer or other processor-containing system that can execute the instructions. In this embodiment, the game is preferably rendered in a three-dimensional manner (even though the display screen itself may only be capable of displaying a flat or two-dimensional image). Such an image can also preferably be rotated or maneuvered in three dimensions, i.e. such that all the faces of the present three-dimensional game can be visualized.

In one embodiment, the present game 1 is presented and solved using a mobile communications device, such as a mobile phone. Mobile communications devices have wireless data transmission and reception functionality (typically using radio frequencies to send and receive data) and a user input device, such as a keypad or a touch screen. The data transfer capability allows a mobile device to receive new puzzles, for example after previously received puzzles are solved by a user. In preferred embodiments the input device is a touch screen, a display that enables the user to interact with the mobile communications device by touching areas on the screen.

In another embodiment, the present game can be illustrated or displayed in two dimensional form, either on paper or on a display screen. In this embodiment, the game is solved by applying the rules of the present game only to the displayed faces, and can resemble for example the faces shown in FIGS. 1 and 4.

Methods of Generating Puzzles

As described above, each face of the present game 1 comprises a matrix of rows and columns determined by the size of the puzzle. For purposes of the following discussion, the cells of the rows and columns of each face are numbered from 1 to a number N. As shown in FIG. 3 (for a face having nine rows and nine columns) and FIG. 6 (for a face having four rows and four columns), the rows can be numbered from 1 at the top to N at the bottom (where N is nine or four, respectively), and the columns can likewise be numbered from one at the left to N at the right. The faces of a game are also preferably addressed in a predetermined order. For example, when the game is in the form of a cube, the faces can be considered in order from top, left, front, right, back and bottom. It is important to orient the faces properly when generating the puzzle as the overlap will require knowing exactly which cells are affected.

FIG. 9 illustrates a simplified process for generating a new 3D Sudoku puzzle. The process is preferably performed by a computer program although it can alternatively be done without the aid of a computer. The first step of the process shown in FIG. 9, step 102, is to create a three-dimensional matrix of cells, one for each symbol to be used in the game. A nine-by-nine cube would have nine rows of nine cells each grouped into each face, for example, in which case the final matrix for the entire cube would be made up of six face groups of eighty-one cells each for a total of four hundred eighty-six cells. A four-by-four cube, alternatively would be made up of four rows of four cells each grouped onto each face, with the final matrix for the entire four-by-four cube comprising six face groups of sixteen cells each for a total of ninety-six cells. Cubes with a larger number of cells on each face can also be used in the present method, as long as the square root of the number is a whole number (e.g., 25, 36, etc.).

As is common in a variety of programming languages, in a preferred embodiment of the puzzle generation process the cells of the matrix of cells are just pointers to the memory locations for individual cells. Cells can be referred to in many programming languages as “objects,” and this “pointer to an object” concept can be used in the next step 104.

In the second step of FIG. 9, step 104, the number of objects to be considered is reduced. The cells of the matrix are systematically reviewed and the pointers are re-pointed so that cells at the corners and edges of a face that logically must share the same number with adjacent cells of another face point to the same memory location. So, for example, the pointers for cells on the top side 23 of the front face 11 and for adjacent cells on the bottom side of the top face 13 point to the same memory location. This systematic approach ensures the number of cells considered for the puzzle is reduced to the minimum number needed.

During remapping, some cells are forced to be mapped in reverse order (N−1) so it is important to understand the direction in which the cells are described. Given the layout of faces described above, e.g., in connection with FIGS. 2 and 5, the cells along the top side 23 of the front face 11 should have the same symbols as the adjacent cells along bottom side of the top face 13, and the cells along the right side 25 of the left face 16 should be the same as the cells along the left side 26 of the front face 11, for example.

When considering each edge, in addition to the order that the cells appear on the edge, once the faces are wrapped around the cube, some edges are inverted in relation to edges on other faces that they line up with. For example, the right side 25 of the top face 13 maps to the top side 23 of the right face 15, however cell number 1 of the right face 15 is cell N of the top face 13, so careful consideration must be given to the direction of each mapping. As this mapping is used to change the pointers in the matrix to point to common memory locations, care must be given to map these cells in a particular order to ensure all pointers are properly accounted for in the mapping.

Table 1 below illustrates the order that each edge should be mapped to ensure that no cell pointers are lost. When this mapping is complete the number of cells considered in a nine-by-nine game is reduced from four hundred eighty-six cells to three hundred eighty-six by overlapping the common edges and corners. Likewise, when generating a four-by-four game, the number of cells considered is reduced from ninety-six cells to fifty-six.

TABLE 1 This edge must point to . . . cells from this edge. Direction Face Direction Face Top Side (1-N) Top Face Top Side (1-N) Back Face Top Side (1-N) Front Face Bottom Side (1-N) Top Face Top Side (1-N) Left Face Left Side (1-N) Top Face Top Side (1-N) Right Face Right Side (1-N) Top Face Left Side (1-N) Right Face Right Side (1-N) Front Face Top Side (1-N) Bottom Face Bottom Side (1-N) Front Face Left Side (1-N) Back Face Right Side (1-N) Right Face Right Side (1-N) Left Face Left Side (1-N) Front Face Bottom Side (1-N) Left Face Left Side (1-N) Bottom Face Bottom Side (1-N) Bottom Face Bottom Side (1-N) Back Face Right Side (1-N) Bottom Face Bottom Side (1-N) Right Face

Step 106 of FIG. 9 is to randomly select a cell 40 to start with. Later steps in the present process in some instances loop back to this point whenever a random cell is needed. For this reason it is advantageous to follow certain rules relating to the selection of a random cell to which a value is assigned.

Solving Sudoku puzzles preferably involves reducing the number of valid choices that there may be for any given cell. In the present process, a list of valid choices for each cell 40 is maintained, and whenever a value is selected for a cell, any other cell in the puzzle that is affected by this selection will have that value removed from its list of valid choices. In step 106, it is advantageous to select a cell from the face in the game with the most open cells (i.e. cells that do not yet have only a single valid choice), and to select on this face the cells having the fewest number of valid choices. In order to accomplish this, it is first necessary to create a list of cells that have the least number of valid choices. If ten cells all have only two numbers as valid selections and no cells have one number as a valid selection then a random cell will be selected from these ten cells with two valid choices.

In the beginning of the process, all cells will have N valid choices, so a random cell is chosen and set to a random value, as described in step 108. In step 110, the value chosen needs to be removed from all cells that are in the same row, column and region as the selected cell. If the cell is on an edge or corner, then any rows, columns and regions on other faces need to be updated, since adjacent cells must comprise the same value, pursuant to the rules of the present game 1. This value is therefore also removed from the list of possible values available to cells that are in the same row, column and region as such adjacent cells.

In step 112, exclusive choices are processed, i.e. remaining cells for which there is only one valid choice are identified. An exclusive choice is an artifact of the way the puzzle is solved, and minimizes the number of random choices the computer will make in coming up with a solution. The first time through the game generation loop no exclusive choices will be found, but it is important to put this step into the process so that exclusive choices can be accounted for.

To identify exclusive choices, each face in the game is preferably processed sequentially, and the validity of each number or other symbol used in the game is tested in each remaining cell (i.e. each cell to which a symbol has not yet been assigned) to see if the cell can be identified as one that has a single valid choice. If one is identified, then it is processed as in step 110 to assign the single valid value to this cell and then remove this value as a valid choice from all concerned cells in the puzzle.

Once cells with only a single valid choice of symbols are removed from the puzzle, the process returns to step 106. Once there are no remaining cells to be solved, the puzzle is checked for validity by applying the Sudoku rules to every row, column and region in the puzzle. If the puzzle is not valid for any reason, then the process is repeated until a valid puzzle is generated.

In step 116, the final step of generating the three dimensional Sudoku puzzle, any cells that were randomly generated in creating the puzzle are retained, i.e. are shown in the puzzle, and all of the cells whose values are set pursuant to the rules of the present game are discarded or hidden from view and are thus not visible to a user of the present game 1. This step generates a puzzle to be solved by such a user which has only one solution.

Although the present invention has been described in considerable detail with reference to certain preferred embodiments, other embodiments are possible. The steps disclosed for the present methods, for example, are not intended to be limiting nor are they intended to indicate that each step is necessarily essential to the method, but instead are exemplary steps only. Therefore, the scope of the appended claims should not be limited to the description of preferred embodiments contained in this disclosure. All references cited herein are incorporated by reference in their entirety. 

1. A three-dimensional Sudoku game comprising: a plurality of faces, each face comprising a plurality of sides, wherein each of the sides comprises an edge shared with a different face; a plurality of cells on each face, wherein the cells of each face are arranged in rows and columns, each row and each column of the face comprising N cells, wherein N is a whole number greater than 1, thereby forming an array of N² cells on each face of the game; and N regions on each face, each region comprising N rows of N cells each and N columns of N cells each, wherein each cell includes no more than one symbol in a non-repeating series of symbols, each symbol in the series of symbols appearing only once in each row, each column, and each region of a face, and wherein a first cell of a first face of the game and a second cell of a second face must include the same symbol if the first cell and second cell are adjacent.
 2. The game of claim 1, wherein the symbols are numbers.
 3. The game of claim 2, wherein the numbers are an ordered series of numbers.
 4. The game of claim 1, wherein N is selected from the group consisting of 4 and
 9. 5. The game of claim 1, wherein each cell is in the form of a square.
 6. The game of claim 5, wherein each row of a face is arranged perpendicularly to each column of the face.
 7. The game of claim 1, wherein each face forms a square and the faces are arranged to form a cube.
 8. The game of claim 1, wherein the plurality of faces is displayed in two dimensions.
 9. The game of claim 1, wherein the game is in physical form.
 10. The game of claim 9, wherein the game is formed from a rigid planar material folded into a three-dimensional object, with each face of the object comprising a face of the game.
 11. The game of claim 9, wherein the game is formed from paper.
 12. The game of claim 1, wherein the game is in the form of an image displayed on a display device.
 13. The game of claim 12, wherein the display device is a mobile communications device comprising a display screen.
 14. A method of playing a three-dimensional Sudoku game, comprising the steps of: providing a plurality of faces which form at least part of a polyhedron, each face comprising a plurality of sides and N regions, each region comprising N rows of N cells each and N columns of N cells each, wherein N is a whole number greater than 1; assigning a different symbol from a group of N² non-repeating symbols to each cell in each row of each face; assigning a different symbol from the group of N² non-repeating symbols to each cell in each column of each face; and assigning a different symbol from the group of N² non-repeating symbols to each cell in each region of the face, wherein at least a first face and a second face of the polyhedron are joined at an edge, and wherein adjacent cells on the first face and the second face are assigned the same symbol from the group of N² non-repeating symbols.
 15. The game of claim 14, wherein the symbols are numbers.
 16. The game of claim 15, wherein the numbers are an ordered series of numbers.
 17. The game of claim 14, wherein N is selected from the group consisting of 4 and
 9. 18. A method of generating a three-dimensional Sudoku game in which each cell of the game can comprise a symbol from a predetermined set of symbols, wherein each symbol of the set appears only once in each row, column, and region of a face of the game, comprising: (a) generating a plurality of faces, each face comprising N² cells, wherein the cells are arranged into rows of N cells and columns of N cells; (b) assigning a top edge, a bottom edge, a right edge, and a left edge to each cell; (c) mapping each cell such that the top edge of a cell is the bottom edge of an adjacent cell in a column and such that a right edge of the cell is the left edge of an adjacent cell in the row; (d) randomly selecting a previously unselected cell of a face of the game and randomly assigning a symbol to the cell from the predetermined set of symbols, thereby generating a randomly assigned cell containing the symbol, wherein the symbol must be different from other symbols contained in other cells in the same row, column and region as the randomly assigned cell, and wherein when the randomly assigned cell shares an edge with a second cell on a different face of the game, the randomly assigned cell and the second cell must comprise the same symbol; (e) selecting a remaining cell in the game and determining whether the remaining cell can comprise only one valid choice of symbols, and if so, assigning the valid symbol to the remaining cell to generate a nonrandomly assigned cell, and removing the valid symbol from the set of predetermined symbols assignable to other cells in the same row, column and region of the nonrandomly assigned cell; and (f) repeating steps (d) and (e) until a symbol from the predetermined set of symbols has been assigned to each cell of the game, thereby generating a solved game.
 19. The method of step 18, further comprising the step after step (f) of removing the symbols from all of the nonrandomly assigned cells of the solved game, thereby generating a three-dimensional Sudoku game with only one solution.
 20. The method of claim 18, wherein N is selected from the group of 4 and
 9. 21. The method of claim 18, wherein step (d) comprises selecting a previously unselected cell from the face of the game comprising the fewest previously selected cells. 